Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8r4)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8r4.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 15/4}, z] == -((7 (4 (12939264000 + 25878528000 Sqrt[z] - 1795496625 z + 73516353300 z^(3/2) - 4193551440 z^2 + 78941977920 z^(5/2) + 31630210560 z^3 - 138229217280 z^(7/2) - 4338524160 z^4 + 17754390528 z^(9/2) + 137035776 z^5 - 551288832 z^(11/2) - 1048576 z^6 + 4194304 z^(13/2) + E^(4 Sqrt[z]) (-12939264000 + 25878528000 Sqrt[z] + 1795496625 z + 73516353300 z^(3/2) + 4193551440 z^2 + 78941977920 z^(5/2) - 31630210560 z^3 - 138229217280 z^(7/2) + 4338524160 z^4 + 17754390528 z^(9/2) - 137035776 z^5 - 551288832 z^(11/2) + 1048576 z^6 + 4194304 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (167418075825 + 328002760800 z + 397579104000 z^2 - 565445836800 z^3 + 71424737280 z^4 - 2208301056 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (167418075825 + 328002760800 z + 397579104000 z^2 - 565445836800 z^3 + 71424737280 z^4 - 2208301056 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(17815893442560 z^(7/2)))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]